Sign changing bubble tower solutions to a slightly subcritical elliptic problem with non-power nonlinearity

2023/06/05 by Shengbing Deng, Yu Fang, Deng, Shengbing +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2306.02973

Abstract

We study the following elliptic problem involving slightly subcritical non-power nonlinearity \-Δu =\frac|u|^{2^*-2}u[ln(e+|u|)]^ε · amp;\rm in Ω,
u= 0 · amp; \rm on ∂Ω, . where Ω is a bounded smooth domain in ℝⁿ, n≥ 3, 2^*=(2n)/(n-2) is the critical Sobolev exponent, ε>0 is a small parameter. By the finite dimensional Lyapunov-Schmidt reduction method, we construct a sign changing bubble tower solution with the shape of a tower of bubbles as ε goes to zero.

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